For the record, I'll make no bones about the debt that I owe to an unnamed
author or authors who produced a remarkably comprehensive overview of Brackett's
Mars, and indeed, of her solar system on the Wikipedia. I've
given the URL's for the Wikipedia articles and highly recommend them.
But I can also claim to have read a fair proportion of her Mars stories.
Following is the complete list of Brackett's Mars or Mars-related tales,
taken from the Wikipedia article, with notations as to the ones I've read.

Sea Kings of Mars (Thrilling Wonder Stories June 1949)
published in book form as

The Sword of Rhiannon (novelette)

Queen of the Martian Catacombs (Planet Stories Summer
1949) published in book form as

The Secret of Sinharat (novel or novelette)

Black Amazon of Mars (Planet Stories March 1951) published
in book form as

People of the Talisman (novel or novelette)

The Last Days of Shandakor (Startling Stories April 1952)
(novelette)

The Ark of Mars (Planet Stories September 1953) later published
as part of the book

Alpha Centauri or Die! (novelette)

Mars Minus Bisha (Planet Stories January 1954) (short
story)

The Road to Sinharat (Amazing Stories May 1963) (novelette)

Purple Priestess of the Mad Moon (The Magazine of Fantasy
and Science Fiction October 1964) (short story)

Of Brackett's core Martian stories, I can claim to have read ten (set out
in boldface), including seven novels or novelettes. I've missed five
core stories, and four peripheral Mars stories, most of these are shorter
works. Still, I think I've got enough of a background to talk
about it. I've missed many of the early Mars stories, but these
are short works, and in my view, these would have been earlier in her career
and probably even closer to Barsoom.

Some notes on the some of the Martian stories: Queen
of the Martian Catacombs and Black Amazon of Mars, were revised
and substantially expanded from stories to novel or novella lengths and
under the titles of People of the Talisman and Secret of Sinharat,
in an Ace Double paperback in 1964, and published again under the book
title Eric John Stark: Outlaw of Mars. Eric John Stark also
featured in a story called the Enchantress of Venus in 1949, which
clearly follows up from the Martian stories, and contains a throwaway reference
to Sinharat.

The Skaith trilogy (The Ginger Star, Hounds of Skaith
and Reavers of Skaith) published between 1974 and 1976, also featured
Eric John Stark, but took place in universe in which humans seem to have
had interstellar travel for some time which is not at
all the case for the other Solar System stories, obviously a parallel universe
Stark (Or possibly, Stark is simply somehow heir to Barsoomian level longevity,
and he's simply lived long enough to see interstellar travel). Stark
and the Star Kings, published in 2005, takes place in Edmond Hamilton's
Star King universe (Brackett was married to Hamilton, and he apparently
also did substantial revisions on the two Outlaw of Mars novels), obviously
another parallel universe (or a very long life). For my purposes, I'm only
referring to the two novels or novellas published in Eric John Stark:
Outlaw of Mars.

Purple Priestess of the Mad Moon, The Road to Sinharat,
Mars
Minus Bisha and the Last Days of Shondakor and the Beast
Jewel of Mars is published collectively as The Coming of the Terrans.

On the other hand, the Sword of Rhiannon and Nemesis from
Terra are full fledged stand alone novels, published singly.

The Halfling is published in a Brackett short story collection
of the same name, which also includes the Enchantress of Venus.
The three or four other stories in the collection are not related to Mars,
Venus or Brackett's solar system. Brackett also edited an anthology,
Best
of Planet Stories, which contains her collaboration with Bradbury ‘Lorelei
of the Red Mist’, set in the same area of Venus as Enchantress of Venus.

The other stories: Interplanetary Reporter, No Man's
Land In Space, Outpost on Io, the Halfling are only tangentially related
to Brackett's Mars. The planet is featured mostly by passing reference,
rather than having its plot intrinsically set there. The
Ark of Mars begins on what is recognizably Brackett's Mars, though
apparently at a distant future time; however, it soon leaves it. Citadel
of Lost Ships is not set on and does not touch directly on Mars at
all, but although I haven't read it, I've included it here for my own reasons.

Appendix 2: Brackett's Venus Stories

In addition to some fourteen Mars stories and novels, Brackett published
a series of Venus stories. The Venus stories were less ambitious,
perhaps seven short stories and novellas among them, nothing approaching
novel length.

The Dragon Queen of Jupiter (Planet Stories Summer 1941)
also published as

The Moon That Vanished (novelette; Thrilling Wonder Stories
October 1948)

Enchantress of Venus (novella; Planet Stories Fall 1949)
also published as

City of the Lost Ones

Of the eight stories, I've read only three of them. In addition,
there were another five stories which touched on or dealt with Venus but
were not focused principally there.

The Stellar Legion (Planet Stories Winter 1940)

The Demons of Darkside (Startling Stories January 1941)

Interplanetary Reporter (Startling Stories May 1941)

No Man's Land in Space (novelette; Amazing Stories July 1941)

Outpost on Io (Planet Stories November/Winter 1942)

It's harder to reconcile Brackett's Venus with the Venus of Kline, Farley
and Burroughs. Barsoom was a towering landmark work.
Amtor was sort of always a weak sister in the Burroughs canon, and hardly
as defining or definitive of Venus as Barsoom was of Mars.
The depiction of Venus seems to have hewed closer to the general narrative
and did not hue nearly so specifically or closely to any one author's vision.

Indeed, there are aspects to Brackett's vision of Venus that seem dramatically
inconsistent with Burroughs or Kline's or Farley's Venuses, and seem much
harder to explain in terms of the political and economic impacts of colonialism
or foreign perspectives. However, without a better look at
more of the Venus stories, its difficult, if not impossible to say anything
with certainty.

The two principle stories or novellas of Venus I've read have been Lorelei
of the Red Mists and Enchantress of Venus. The Halfling
is set on Earth, but features Venusian animals and references, among others.
Both of the principal stories focus on a large lake or inland sea in highlands
sheltered by a mountain range which has the unique character of being filled,
not with water, but with a heavy gas which is thick enough to swim in and
to float boats, the gas is so suffused with oxygen that it is breathable.
In terms of the real Venus, or the collective Burroughs/Kline/Farley map,
this would probably be located inland of the equatorial continent, along
the central mountain range. The people around this sea seem
to be closest ethnically to Kline's Zarovians. Brackett's Venus,
and they seem to speak a universal planetary language, consistent with
the other writers.

Referred to from the Wikipedia article are forms of Plant Men who seem
roughly analogous to Burroughs Brokols, as well as Amphibian Men who might
be loosely related to the Lu of Caprona, to Burroughs Myposans or Kline's
Toad Men of Venus.

And that's all that I can really say. The simple fact is
that Brackett's Venus work is much smaller than her Mars, and I've read
comparatively less of it.

Appendix 3: The Moon Maid Conflict

Although Brackett works well in terms of giving us a picture of Barsoom
and its experience with western colonialism, we do have a problem in that
events seem to diverge from Burroughs Moon Man stories.

Its tricky. As I've noted, in Brackett, the dates given for titles
of her collection ‘The Coming of the Terrans’ suggest that Earth
may have been exploring space or establishing relations with Mars as early
as the 1980s or 1990s. Presumably communication might have begun
even before that, perhaps as early as the 1960s.

On the other hand, I've questioned this, putting a guess for Mars colonial
period as late as the 22nd to 23rd or 24th centuries.

If you look at the chronology of Burroughs Moon Maid series, it seems
pretty incompatible. Formal communication begins around 1967, which
we can reconcile with Brackett.

But then, the efforts at space travel, by Barsoom is in 2015.
In 2024 and 2026, Earth ships attempt to reach Barsoom, but fail to make
it. We have Julian and Orthis fighting it out in The Moon Maid.
This is obviously completely inconsistent with the dates put forward in
Coming
of the Terrans since in those dates, Earth's influence is well established
on Mars.

To make matters worse, in the Moon Man, Orthis invades and conquers
Earth (or at least North America) in 2050. This domination
extends up until the 25th century. This seems completely incompatible
with the events and references in Brackett's solar system stories, which
have Earth being active in dominating the rest of the solar system, and
in particular, North America being a key industrial and political player
in Earth. There are several references to New York.

There are some possible resolutions. One is to simply suggest
that the Moon Maid series never happened. It was related
to us as prophecy, with people in a ‘real time’, relating the prophetic
flashbacks from their future descendants lives. So, the obvious
solution is that with forewarning, people changed their actions and the
events never came to pass. Indeed, that might have been the
whole point of the characters relating their stories to Burroughs who is
in these fictions, initially a successful and widely read writer, and later
in the beginning of the Moon Man, a high government official.
In either role, he might well have derailed this potential future.

Or we could argue that the Brackett Mars never happened, obviously because
its written by Burroughs. So only Burroughs fits in the Burroughs
Universe. Original author trumps.

Another approach is to simply say that the Moon Maid series and
the Colonial Barsoom stories are simply two different parallel worlds,
springing from John Carter's original timeline.

Or, perhaps the wildest theory is to accept the Moon Maid sequence,
and Brackett's Mars as both taking place in the same Universe.
On this line, what we'd argue is that although the Kalkars conquered, their
conquest was restricted to North America. The rest of the world,
particularly Europe, England and Australia, went along on its merry way.
Perhaps some enclaves of North America, like New York, continued on in
the modern fashion. Or perhaps refugees from America founded
a new New York or N'York in Australia or Latin America. As
Earth dominated the solar system, the Kalkars in North America grew increasingly
feudal and backwards? Ridiculous? Perhaps.
But we do have the example of Eastern Europe and Ceaucescu's Romania, which
grew increasingly feudal and backwards while other parts of the world moved
forward.

In any event, I'm just tossing it out there. The reader
who cares can make their own judgments and draw their own conclusions.